Problem: Simplify to lowest terms. $\dfrac{42}{30}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 42 and 30? $42 = 2\cdot3\cdot7$ $30 = 2\cdot3\cdot5$ $\mbox{GCD}(42, 30) = 2\cdot3 = 6$ $\dfrac{42}{30} = \dfrac{7 \cdot 6}{ 5\cdot 6}$ $\hphantom{\dfrac{42}{30}} = \dfrac{7}{5} \cdot \dfrac{6}{6}$ $\hphantom{\dfrac{42}{30}} = \dfrac{7}{5} \cdot 1$ $\hphantom{\dfrac{42}{30}} = \dfrac{7}{5}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{42}{30}= \dfrac{2\cdot21}{2\cdot15}= \dfrac{2\cdot 3\cdot7}{2\cdot 3\cdot5}= \dfrac{7}{5}$